Question

(04.04r mc)
the golf clubs have been sorted into woods and irons. the number of irons is four more than two times the number of woods. the equipment is 75% irons. how many woods are there?
4
5
6
7

Explanation:

Step1: Define Variables

Let \( w \) be the number of woods, and \( i \) be the number of irons. From the problem, \( i = 2w + 4 \). The total number of golf clubs is \( w + i \), and irons are 75% of the total, so \( i = 0.75(w + i) \).

Step2: Substitute \( i \) in the Percentage Equation

Substitute \( i = 2w + 4 \) into \( i = 0.75(w + i) \):
\( 2w + 4 = 0.75(w + 2w + 4) \)
Simplify the right - hand side: \( w + 2w+4=3w + 4 \), so \( 2w + 4 = 0.75(3w + 4) \)

Step3: Solve the Equation

Expand the right - hand side: \( 2w+4 = 2.25w+3 \)
Subtract \( 2w \) from both sides: \( 4=0.25w + 3 \)
Subtract 3 from both sides: \( 0.25w=1 \)
Multiply both sides by 4: \( w = 4 \)

We can also check by plugging in the options:

• For \( w = 4 \): \( i=2\times4 + 4=12 \). Total clubs \( = 4 + 12 = 16 \). \( 12\div16 = 0.75=75\% \), which matches.
• For \( w = 5 \): \( i = 2\times5+4 = 14 \). Total \( = 5 + 14 = 19 \). \( 14\div19\approx0.737

eq0.75 \)

• For \( w = 6 \): \( i=2\times6 + 4 = 16 \). Total \( = 6+16 = 22 \). \( 16\div22\approx0.727

eq0.75 \)

• For \( w = 7 \): \( i=2\times7 + 4 = 18 \). Total \( = 7 + 18 = 25 \). \( 18\div25 = 0.72

eq0.75 \)

Answer:

A. 4